How to calculate the false positives and negatives?
Yes, you can use sklearn's confusion_matrix. To explicitly extract the false positives and negatives, you can do

from sklearn.metrics import confusion_matrix

y_true = [0, 1, 0, 1]
y_pred = [1, 1, 1, 0]
tn, fp, fn, tp = confusion_matrix(y_true, y_pred).ravel()